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Gödel's Solution to Einstein's Field Equations
- oh_sigh 5y agoThis article might have better discussion around it if you could read beyond the first sentence.
- art_kimides 5y agoanyone have a password they can share?
- art_kimides 5y agoOn second thought, since the author is taking advantage of HN to advertise their product, perhaps they should consider making more of the essay available so that potential customers can ascertain they aren't purchasing click bait or some inane twiddle twaddle.
- fxj 5y agohttps://en.wikipedia.org/wiki/G%C3%B6del_metric https://en.wikipedia.org/wiki/G%C3%B6del_metric This solution has many unusual properties—in particular, the existence of closed timelike curves that would allow time travel in a universe described by the solution. Its definition is somewhat artificial in that the value of the cosmological constant must be carefully chosen to match the density of the dust grains, but this spacetime is an important pedagogical example. The solution was found in 1949 by Kurt Gödel. The Gödel metric is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles (dust solution), and the second associated with a nonzero cosmological constant (see lambdavacuum solution). It is also known as the Gödel solution or Gödel universe. Following Gödel, we can interpret the dust particles as galaxies, so that the Gödel solution becomes a cosmological model of a rotating universe. Besides rotating, this model exhibits no Hubble expansion, so it is not a realistic model of the universe in which we live, but can be taken as illustrating an alternative universe, which would in principle be allowed by general relativity (if one admits the legitimacy of a nonzero cosmological constant). Less well known solutions of Gödel's exhibit both rotation and Hubble expansion and have other qualities of his first model, but travelling into the past is not possible. According to S. W. Hawking, these models could well be a reasonable description of the universe that we observe, however observational data are compatible only with a very low rate of rotation.[4] The quality of these observations improved continually up until Gödel's death, and he would always ask "is the universe rotating yet?" and be told "no, it isn't".[5] Many other exact solutions that can be interpreted as cosmological models of rotating universes are known. See the book Homogeneous Relativistic Cosmologies (1975) by Ryan and Shepley for some of these generalizations.
- mam3 5y agoGreat idea to send us on a paid page of your own product. Worst ad ever